Preface 1 Introduction 1.1 Phase transitions and order parameters 1.2 Models: Ising, XY, Heisenberg 1.3 Universality and critical exponents 1.4 Scaling of free energy 1.5 Correlations and hyperscaling 2 Ginzburg-Landau-Wilson theory 2.1 Partition function for interacting bosons 2.2 Bose-Einstein condensation 2.3 Hartree approximation 2.4 Landau's mean-field theory 2.5 Upper critical dimension 3 Renormalization group 3.1 Idea 3.2 Momentum-shell transformation 3.3 E-expansion 3.4 Dangerously irrelevant coupling 3.5 Corrections to scaling 3.6 Field-theoretic perspective 3.7 Computation of anomalous dimension 3.8 Summary 4 Superconducting transition 4.1 Meissner effect 4.2 Fluctuation-induced first-order transition 4.3 Type-II superconductors near four dimensions 4.4 Anomalous dimension for the gauge field 4.5 Width of the critical region 5 Near lower critical dimension 5.1 Goldstone modes 5.2 Mermin-Wagner-Hohenberg theorem 5.3 Non-linear σ-model 5.4 Low-temperature expansion 5.5 Discussion 6 Kosterlitz-Thouless transition 6.1 Vortices and spin waves 6.2 Mean-field theory 6.3 Duality and the sine-Gordon theory 6.4 Renormalization of the sine-Gordon model 6.5 Universal jump of superfluid density 6.6 Heisenberg model 7 Duality in higher dimensions 7.1 Frozen lattice superconductor 7.2 Confinement of magnetic monopoles 7.3 Magnetic field correlations 7.4 Compact electrodynamics 8 Quantum phase transitions 8.1 Dynamical critical exponent 8.2 Quantum critical point in ~4-theory 8.3 Bose-Hubbard model
8.4 Quantum fluctuations and the superfluid density 8.5 Universal conductivity in two dimensions Appendix A Hubbard-Stratonovich transformation Appendix B Linked-cluster theorem Appendix C Gauge fixing for long-range order Select bibliography Index
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